Abstract
I was invited to give a talk this past July at an interdisciplinary meeting in the beautiful smokey mountains of Tennessee. I chose to speak on the subject of the 'structure of consciousness'. The event was attended by a small group of individuals from various fields - including philosophy, psychology, and physics. Brian Greene, a renowned physicist and a specialist in quantum field theory, made a presentation on current cutting-edge work in 'string theory' - a subject which happens also to be the topic of his new book, The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory. 1 After his talk, I engaged Brian in a conversation on what appeared to me to be an interesting resemblence between how he seemed to be approaching the structure of reality and what some of us want to say about the structure of consciousness.
It is on this conversation that I wish to report in this piece.
Section One - Liminocentric Structures
In our recent series Pat and I discussed the role that the mandala, as symbol of a profound organizing principle, plays in personality typologies. This required us to articulate our views on the structure of consciousness itself. If the mandala is
structured in such a way that its 'outermost' rim must be conceived as identical to
its 'innermost' center, we argued, this is because consciousness is similarly structured.
If conceived as a series of ever-wider experiential contexts, nested one within the other like a set of Chinese boxes, consciousness can be thought of as wrapping back around on itself in such a way that the outermost 'context' is indistinguishable from
the innermost 'content' - a structure for which we coined the term 'liminocentric'.
As attention expands its focus to include more and more of the margin or 'fringe' of consciousness, awareness becomes increasingly diffuse and undifferentiated. This is identical to what happens when, moving in the opposite direction, the scope of attention is progressively concentrated toward an innermost limit or 'center', which must ultimately be recognized as 'empty' - ie, also undifferentiated, or 'without object'. 2 The same mental state, which occurs at both extremes, is a highly significant state in meditation practice, repeatedly singled out for special consideration by mystics in various traditions.
As it turns out, string theory may conceive of the structure of physical reality in a remarkably similar way.
The meeting that took place in Tennessee was the brain-child of C.O. Evans, an early pioneer in consciousness studies, who was also present for the proceedings and an active participant. A philosopher of mind and science, Dr. Evans has advocated a trans-disciplinary approach to consciousness studies from the very beginning of his career in the 1960s. Every aspect of the week-long conference, which was exquisitely designed, contributed to an environment that stimulated creativity and collaboration. It was a rather remarkable event, by all accounts.
I was a student of Dr. Evans in the early days, and then worked with him to
present a 'model of consciousness' based on his ground-breaking earlier work.
He had proposed, amongst other things, that consciousness has a complexity
that lends itself to being described as 'structured'. He was indeed
the first to specifically propose that consciousness is 'structured by
attention'. 3 I shall
not go into this model in further detail here, since I have elaborated
on it in Section-2 of another paper in this Issue, 'The Structure of Consciousness - Liminocentricity, Enantiodromia, and Personality'. Also,
Dr. Evans's work has recently been made directly available at
www.mentalstates.net.
What I WOULD like to do at this point, however, is mention that it was Cedric's work
that first prompted me, in the 1970s, to begin to explore how the structure of
consciousness might best be described. Once one conceives of consciousness as 'structured', as one professional philosopher participating in the recent meeting in Tennessee put it, then it is only natural to begin to think in terms of using complex topologies to describe that structure. And that is precisely what I endeavored to do back then. This led me, at the
time, to propose a torus-like 4 structure which we have only recently begun to use the term 'liminocentric' to describe.
Section Three - String Theory and 'Extra' Dimensions
The few courses in relativity and quantuum mechanics which I had as an undergraduate
in aeronautical engineering probably gave me a better than average exposure to
physics. It at least prepared me to appreciate the basic issues with which Brian, as a
string theorist, is grappling - the search for a theory that can reconcile
'general relativity', the field of physics that deals with very large distances and events, and 'quantum mechanics', the field of physics that seeks to understand events at small sub-atomic distances. It was Einstein, of course, who gave us the theory of general relativity, which successfully applied topology to the four-dimensional 'space-time continuum' that he introduced to the world. And it was he who showed us all how such a surface might warp - resulting in various strange phenomena like 'black holes'. But despite such monumental accomplishments, Einstein sought in vain for a theory that could unify general
relativity and quantum mechanics.
His failure, which was surely a personal disappointment, also had larger ramifications. Since general relativity theory and quantum mechanics can't both be right, physicists have been living under the dark cloud of apparently contradictory views about the nature of physical reality for nearly a century now.
So it is with a great sense of excitement that theorists like Brian Greene
anticipate that 'string theory' is quite close to providing the final solution to this chronic dilemma in physics. Lets have a quick look at why string theory seems so
promising.
The basic idea behind the theory is described in the following way by Greene:
This drastic change in how string theory would have us describe
the interaction of objects on the shortest of distance scales is what
promises to reconcile quantum mechanics and general relativity.
But there is also 'a price to be paid' for this approach, according to Greene.
'The equations of string theory are self consistent only if the universe contains, in addition to time, nine spatial dimensions', he explains. And this, he admits,
is 'in gross conflict' with the fact that we perceive the physical space in which
we live as a world having only THREE spatial dimensions.
In an attempt to deal with this apparent discrepancy string theorists
explain that the additional six dimensions not only wrap back on themselves,
but do this in extremely short distances (of approximately 10-33 cm)
which make them too tiny for us to see, even if we use the most advanced technology
that is currently available to us, like the accelators mentioned in the above
passage.
It is with the assumption about the presence of extra hidden dimensions
that the real fun begins, it seems to me. For it is at this juncture in the
argument that subtle shifts are bound to be introduced into the very concept of 'dimensionality'. And these will invariably impact on the language available to
us for describing non-physical spaces, such as the psychological or experiential
'space' in which consciousness can be conceived as 'existing' and having a
'structure'.
Other physicists who are seeking a solution to the same problem as Greene
put forward rival models with slightly different features. It cannot be said
for certain which of the models will ultimately prevail. But most do share
a common assumption - the assumption of extra physical 'dimensions'.
Theorists who want to make this assumption must, like Greene, try to account
for the apparent absence of these additional dimensions in the world as we
perceive it. In doing this they will need to address the philosophical issues
that such strategies in theory-construction inevitably kick up - What does
it mean, for instance, for a space to 'have' dimensions in the first place? And
what kind of relationship is it conceptually permissible for one 'dimension' of
a given 'space' to have with respect to another 'dimension'?
The idea of physical space having more than 3 dimensions is not a new idea.
Nor is it new to speculate that the extra physical dimensions have not been
observed because they must be 'too small to see'. In a web site entitled 'Hyperspheres, Hyperspace, and the Fourth Spatial Dimension - A New Look at the Universe as a Closed Cosmic Hypersphere', Michael Feltz tells us that
While a fourth spatial dimension was hypothesized several times during the 19th
century, the first serious proponent of its existence in the 20th century was an unknown Prussian mathematician named Theodor Kaluza.
In 1919 Kaluza wrote a letter to Albert Einstein suggesting that, should there be a fourth spatial dimension, then gravity and electromagnetic radiation were basically different manifestations of the same underlying entity. It took Einstein until
1921 before he replied to Kaluza's remarkable suggestion with a belated agreement.
But if there was a fourth spatial dimension, why didn't we notice it?
In 1926 a Swedish mathematician named Oskar Klein came up with the first pragmatic answer: a fourth spatial dimension did exist, but in packets of space too small for us to detect. A "compactified" unit of such space is sometimes called the "Kaluza-Klein bottle", and it is the basis for modern string theory.
The Big, the Small, and the Undetectable
But if there are physical dimensions that are 'too small to see', isn't
it possible that there may also be dimensions 'too large to see'? 5 Precisely this question was posed to Greene by an unidentified audience member in a lecture that he delivered this summer, which I
happened to catch on CSPAN one morning after the conference in Tennessee. His answer
was interesting. 'Well,' he said,
Brian made a similar point in the conversation that I had with him, and it was this that piqued my interest. For it is this feature that seems to suggest that the DIMENSIONS of physically reality are related in such a way that the 'space' in which the physical world exists may itself be liminocentrically organized.
Let me explain.
Brian began the presentation that he gave in Tennessee with a video sequence that illustrated the relationship between the frames that are associated with the tremendously large-scale world of astronomy and the frames associated with the very smallest microscopic scales,
which are the province of quantuum mechanics. Looking at the video it was as if you were watching a series of slides. Each slide zoomed in from one frame to the next smallest frame nested within it, and then again to an even smaller frame within that one, and so on. It looked something like this (click here). In Brian's slides the frames are organized in a heirarchically nested series and after zooming inward a dozen or more times one gets to the very smallest frame and that is the end of the process. In my comparatively simple animation it only takes THREE inward-zooming steps to move from the largest frame to the smallest, but the principle is the same. And I have no way of showing the frenetic, turbulent forms that the space-time continuum
displays, in his video, at the level of the very smallest frame. 6
But the simple animation that I present here will suffice to suggest why I was intrigued by Brian's animation, given the fact that I am apt to conceive of consciousness as also comprised of a series of nested frames - as the reader will know if he or she has read other articles at this site. In the conversation I had with Brian I pointed out this obvious similarity. I was careful to mention, however, that according to my view about how consciousness may be structured, the process does not end when one arrives at the smallest frame. Rather, since the smallest frame in the series of nested frames is identical to the largest, the whole structure loops back on itself. Like this (click here). In a liminocentrically organized structure, such as the one depicted in this second animation, the series of concentrically nested frames thus constitutes a never-ending cycle.
So, I asked Brian, wasn't this where the parallel between how he was using his set of nested
frames and how I was using mine broke down? To my surprise, he cautioned
me not to be so sure.
The Big, the Small, and the Indistinguishable
Michio Kaku, also an internationally recognized authority in theoretical physics, describes Dr. Greene's book as a "delightful, lucid introduction to the greatest problem in all of physics, the quest to unify all the laws of nature".
Skeptical, and not wanting to leap to conclusions, I offered the view that he was probably using 'identity' in a somewhat metaphorical sense. I, in contrast, had in mind something
more literal. Only if the center (smallest dimension) and the periphery (largest dimension) of the structure were ACTUALLY identical - i.e., indistinguishable - should we speak of a liminocentric structure. But, again to my surprise, he assured me that he was speaking about just such an indentity between the very small and very large.
Later, when I had the opportunity to look at his Chapter 10, I saw what
he was talking about. For according to string theory, a circular dimension with a
radius of R is actually identical to a circular dimension with a radius of 1/R, which leads to what Greene refers to in his book as 'the R and 1/R physical identification of string theory'. 7 With this definition in mind, consider the following passage from his book -
If you have RealPlayer installed on your computer, you can hear a lecture of Brian Greene's
on "Schedule Aspects of D-branes on Curved Space", by clicking on the title above. Although his book is
very easy to follow, and does not use technical language, the above lecture was not
intended for the general public. What is a D-brane?
On Tuesdays at 1:00 PM Pacific Standard Time, you can also hear Michu Kaku's weekly hour-long radio show, "Explorations in Science" broadcast live on the internet from WKPFA.
And even if consciousness and the physical world CAN be conceived as having the same general structure? So what? That was the question that seemed to occur to both of us at that point in the conversation. The question was asked, and we stared blankly at one another for a moment. For Brian, the physicist involved in a study of the material world, the concept of consciousness admittedly plays hardly any role whatsoever. For me, on the other hand, if such a parallel does in fact exist, I would probably be inclined to view this as suggesting
that what we are capable of seeing in the physical world is a function of how the consciousness with which we experience it is structured. Anybody with a background in philosophy will recognize this as a kind of 'neo-kantian' view, perhaps.
1.
Brian R. Greene, The elegant universe - superstrings, hidden dimensions, and
the quest for the ultimate theory (New York:W.W. Norton & Co., Inc., 1999).
2. If the outermost and innermost frames in
the nested series of frames that comprise consciousness are identical and
indistinguishable this would be a fact that is normally lost on us, as
consciousness is rendered 'undifferentiated' at these extremes. But although
it is only in the 'mystical' experience that these extreme states are explored,
it is by virtue of these experiences that mystics tend to want to describe
consciousness as paradoxically (i.e., liminocentrically) structured.
3. C.O. Evans, The subject of consciousness (New York:Humanities Press, 1970).
4. At the time that I was an undergraduate in aeronautical engineering, the
torus was a shape in which researchers who were studying vorticular turbulent air flow had a special interest. These studies were later to become part of the body of work that we now know as 'chaos science'.
More recently, the torus again appeared - as one of the shapes that the tiny extra
dimensions in which vibrate the loops of 'string' that 'string theory' posits. A 'curved space' model utilizing the torus is being used in contemporary physics to describe both the structure of the atom and the structure of the universe, as the following passage
indicates -
Imagine in front of you a torus (a donut-like object), about the size of a small wheel - nine inches or a foot in diameter. Envision it made of some flexible rubber-like material. Put your two thumbs together into the hole of such a torus, so that your remaining fingers naturally wrap around its outside wall. Then swivel both hands at the wrist so that your thumbs pull back toward your body and your fingers push through the center of the hole and point toward you. Your fingers, which were once positioned at the outermost edge of the torus, are now at the innermost center of the torus. And your thumbs, once at the innermost center of the hole have pulled back and are now at the torus's outermost edge. If this motion were made continuous (which is difficult to do with your hands only because they are attached to your arms and can't continue to twist in this manner) the torus would be in the process of continually turning itself inside out. This movement might look something like this (click here) using a two-dimensional animation. Compare this animation to the other two animations in this paper.
5. Not all theories propose that the 'extra' dimensions
will be 'too small to see'.
... Similarly there's an intriguing structure in topology known as a "four-space hypersphere". Three spatial dimensions are obvious to its inhabitants and seem to exist at right angles to each other. Not noticed by its inhabitants, a less obvious fourth spatial dimension causes the three clearly recognizable spatial dimensions to lose their apparent orthogonal relationship eventually. On a global scale the four-space hypersphere has curved space, although it doesn't seem to be curved in the local vicinity any more than the lower-dimensional spherical surface does.
When a universe with a fourth spatial dimension is referred to in the popular literature, it is this character - the one used in topology - that is being referred to, and this is the way I will use it in the following essays. Although most researchers do not think it's possible for this model to exist, I'm going to explain some unique topological assumptions we could make (in Essay #3) so that it does exist. Hyperspheres, Hyperspace, and the Fourth Spatial Dimension - A New Look at the Universe as a Closed Cosmic Hypersphere,
by Michael R. Feltz
6. Greene describes the 'trubulent warp' in the space-time continuum that occurs at this smallest of levels, as a 'frenetic, undulating form'. This description at first glance appears to disagree with Einstein's view of the space-continuum as warped in a gently curving manner. The apparent contradiction, however, is - in a nutshell - the problem that it looks like string theory is capable of addressing.
7. Brian R. Greene, The elegant universe - superstrings, hidden dimensions, and
the quest for the ultimate theory (New York:W.W. Norton & Co., Inc., 1999), page
247.
8. Greene DOES want to explain away these curious ramifications of string theory,
it seems to me. The argument he uses involves him in a fairly detailed and sophisticated analysis of the definition of 'distance', one which permits him to distinguish
TWO types of distance, disintinquishable in terms of very subtly
different operational definitions.
But I am not convinced that his explanation solves the problem with which he
started, as he winds up having to say things about 'size' and 'distance' that seem
just as confusing (if not downright paradoxical) as what he is trying to avoid
saying about the identify of large and small dimensions -
9. A description of 'd-branes' (the membranous surfaces on which 'strings' can end),
from a page at a Harvard web site -
Especially important to M theory is a special type called a D-brane,
named for the 19th century mathematician Peter Dirichlet. In 1995, Dr.
Joseph Polchinsky of the University of California at Santa Barbara showed
that D-branes, which also come in as many as nine dimensions, described
surfaces on which strings can end. But these surfaces are more than mere
boundaries: D-branes are now seen as entities at least as fundamental as
strings. According to a controversial version of M theory called Matrix
theory, D-branes may be the fundamental objects from which strings and
everything else is made.
The Universe
... Maldacena's work also supports a hot new theory that the universe is
holographic. In laser holography, a three-dimensional object is projected
onto a two-dimensional plane, retaining the richness of the original image.
In the Maldacena model, the four-dimensional field theory can be thought
of as a holographic projection of the five-dimensional string theory
(remember that the other five dimensions are rolled up and tucked away).
In a holographic universe, the information about everything in a volume of
space would be displayed somehow on its surface. The bizarre
implications of this notion are only beginning to unfold. Almost in Awe, Physicists Ponder
'Ultimate' Theory, by George Johnson
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